void computeReferenceF(clFFT_SplitComplex *out, clFFT_Dim3 n,
unsigned int batchSize, clFFT_Dimension dim, clFFT_Direction dir)
{
FFTSetup plan_vdsp;
DSPSplitComplex out_vdsp;
FFTDirection dir_vdsp = dir == clFFT_Forward ? FFT_FORWARD : FFT_INVERSE;
unsigned int i, j, k;
unsigned int stride;
unsigned int log2Nx = (unsigned int) log2(n.x);
unsigned int log2Ny = (unsigned int) log2(n.y);
unsigned int log2Nz = (unsigned int) log2(n.z);
unsigned int log2N;
log2N = log2Nx;
log2N = log2N > log2Ny ? log2N : log2Ny;
log2N = log2N > log2Nz ? log2N : log2Nz;
plan_vdsp = vDSP_create_fftsetup(log2N, 2);
switch(dim)
{
case clFFT_1D:
for(i = 0; i < batchSize; i++)
{
stride = i * n.x;
out_vdsp.realp = out->real + stride;
out_vdsp.imagp = out->imag + stride;
vDSP_fft_zip(plan_vdsp, &out_vdsp, 1, log2Nx, dir_vdsp);
}
break;
case clFFT_2D:
for(i = 0; i < batchSize; i++)
{
for(j = 0; j < n.y; j++)
{
stride = j * n.x + i * n.x * n.y;
out_vdsp.realp = out->real + stride;
out_vdsp.imagp = out->imag + stride;
vDSP_fft_zip(plan_vdsp, &out_vdsp, 1, log2Nx, dir_vdsp);
}
}
for(i = 0; i < batchSize; i++)
{
for(j = 0; j < n.x; j++)
{
stride = j + i * n.x * n.y;
out_vdsp.realp = out->real + stride;
out_vdsp.imagp = out->imag + stride;
vDSP_fft_zip(plan_vdsp, &out_vdsp, n.x, log2Ny, dir_vdsp);
}
}
break;
case clFFT_3D:
for(i = 0; i < batchSize; i++)
{
for(j = 0; j < n.z; j++)
{
for(k = 0; k < n.y; k++)
{
stride = k * n.x + j * n.x * n.y + i * n.x * n.y * n.z;
out_vdsp.realp = out->real + stride;
out_vdsp.imagp = out->imag + stride;
vDSP_fft_zip(plan_vdsp, &out_vdsp, 1, log2Nx, dir_vdsp);
}
}
}
for(i = 0; i < batchSize; i++)
{
for(j = 0; j < n.z; j++)
{
for(k = 0; k < n.x; k++)
{
stride = k + j * n.x * n.y + i * n.x * n.y * n.z;
out_vdsp.realp = out->real + stride;
out_vdsp.imagp = out->imag + stride;
vDSP_fft_zip(plan_vdsp, &out_vdsp, n.x, log2Ny, dir_vdsp);
}
}
}
for(i = 0; i < batchSize; i++)
{
for(j = 0; j < n.y; j++)
{
for(k = 0; k < n.x; k++)
{
stride = k + j * n.x + i * n.x * n.y * n.z;
out_vdsp.realp = out->real + stride;
out_vdsp.imagp = out->imag + stride;
vDSP_fft_zip(plan_vdsp, &out_vdsp, n.x*n.y, log2Nz, dir_vdsp);
}
}
}
break;
}
vDSP_destroy_fftsetup(plan_vdsp);
}
/* Demonstrate the complex one-dimensional in-place FFT, vDSP_fft_zip.
The in-place FFT writes results into the same array that contains the
input data. This may be faster than an out-of-place routine because it
uses less memory (so there is less data to load from memory and a
greater chance of keeping data in cache).
*/
static void DemonstratevDSP_fft_zip(FFTSetup Setup)
{
/* Define a stride for the array be passed to the FFT. In many
applications, the stride is one and is passed to the vDSP
routine as a constant.
*/
const vDSP_Stride SignalStride = 1;
// Define a variable for a loop iterator.
vDSP_Length i;
// Define some variables used to time the routine.
ClockData t0, t1;
double Time;
printf("\n\tOne-dimensional complex FFT of %lu elements.\n",
(unsigned long) N);
// Allocate memory for the arrays.
DSPSplitComplex Signal;
Signal.realp = malloc(N * SignalStride * sizeof Signal.realp);
Signal.imagp = malloc(N * SignalStride * sizeof Signal.imagp);
if (Signal.realp == NULL || Signal.imagp == NULL)
{
fprintf(stderr, "Error, failed to allocate memory.\n");
exit(EXIT_FAILURE);
}
/* Generate an input signal. In a real application, data would of
course be provided from an image file, sensors, or other source.
*/
const float Frequency0 = 400, Frequency1 = 623, Frequency2 = 931;
const float Phase0 = .618, Phase1 = .7f, Phase2 = .125;
for (i = 0; i < N; ++i)
{
Signal.realp[i*SignalStride] =
cos((i * Frequency0 / N + Phase0) * TwoPi)
+ cos((i * Frequency1 / N + Phase1) * TwoPi)
+ cos((i * Frequency2 / N + Phase2) * TwoPi);
Signal.imagp[i*SignalStride] =
sin((i * Frequency0 / N + Phase0) * TwoPi)
+ sin((i * Frequency1 / N + Phase1) * TwoPi)
+ sin((i * Frequency2 / N + Phase2) * TwoPi);
}
// Perform an FFT.
vDSP_fft_zip(Setup, &Signal, SignalStride, Log2N, FFT_FORWARD);
/* Prepare expected results based on analytical transformation of
the input signal.
*/
DSPSplitComplex Expected;
Expected.realp = malloc(N * sizeof Expected.realp);
Expected.imagp = malloc(N * sizeof Expected.imagp);
if (Expected.realp == NULL || Expected.imagp == NULL)
{
fprintf(stderr, "Error, failed to allocate memory.\n");
exit(EXIT_FAILURE);
}
for (i = 0; i < N; ++i)
Expected.realp[i] = Expected.imagp[i] = 0;
// Add the frequencies in the signal to the expected results.
Expected.realp[(int) Frequency0] = N * cos(Phase0 * TwoPi);
Expected.imagp[(int) Frequency0] = N * sin(Phase0 * TwoPi);
Expected.realp[(int) Frequency1] = N * cos(Phase1 * TwoPi);
Expected.imagp[(int) Frequency1] = N * sin(Phase1 * TwoPi);
Expected.realp[(int) Frequency2] = N * cos(Phase2 * TwoPi);
Expected.imagp[(int) Frequency2] = N * sin(Phase2 * TwoPi);
// Compare the observed results to the expected results.
CompareComplexVectors(Expected, Signal, N);
// Release memory.
free(Expected.realp);
free(Expected.imagp);
/* The above shows how to use the vDSP_fft_zip routine. Now we
will see how fast it is.
*/
/* Zero the signal before timing because repeated FFTs on non-zero
data can cause abnormalities such as infinities, NaNs, and
subnormal numbers.
*/
for (i = 0; i < N; ++i)
Signal.realp[i] = Signal.imagp[i] = 0;
// Time vDSP_fft_zip by itself.
t0 = Clock();
for (i = 0; i < Iterations; ++i)
vDSP_fft_zip(Setup, &Signal, SignalStride, Log2N, FFT_FORWARD);
t1 = Clock();
// Average the time over all the loop iterations.
Time = ClockToSeconds(t1, t0) / Iterations;
printf("\tvDSP_fft_zip on %lu elements takes %g microseconds.\n",
(unsigned long) N, Time * 1e6);
// Release resources.
free(Signal.realp);
free(Signal.imagp);
}
void benchmark_ffts(int N, int cplx) {
int Nfloat = (cplx ? N*2 : N);
int Nbytes = Nfloat * sizeof(float);
float *X = pffft_aligned_malloc(Nbytes), *Y = pffft_aligned_malloc(Nbytes), *Z = pffft_aligned_malloc(Nbytes);
double t0, t1, flops;
int k;
int max_iter = 5120000/N*4;
#ifdef __arm__
max_iter /= 4;
#endif
int iter;
for (k = 0; k < Nfloat; ++k) {
X[k] = 0; //sqrtf(k+1);
}
// FFTPack benchmark
{
float *wrk = malloc(2*Nbytes + 15*sizeof(float));
int max_iter_ = max_iter/pffft_simd_size(); if (max_iter_ == 0) max_iter_ = 1;
if (cplx) cffti(N, wrk);
else rffti(N, wrk);
t0 = uclock_sec();
for (iter = 0; iter < max_iter_; ++iter) {
if (cplx) {
cfftf(N, X, wrk);
cfftb(N, X, wrk);
} else {
rfftf(N, X, wrk);
rfftb(N, X, wrk);
}
}
t1 = uclock_sec();
free(wrk);
flops = (max_iter_*2) * ((cplx ? 5 : 2.5)*N*log((double)N)/M_LN2); // see http://www.fftw.org/speed/method.html
show_output("FFTPack", N, cplx, flops, t0, t1, max_iter_);
}
#ifdef HAVE_VECLIB
int log2N = (int)(log(N)/log(2) + 0.5f);
if (N == (1<<log2N)) {
FFTSetup setup;
setup = vDSP_create_fftsetup(log2N, FFT_RADIX2);
DSPSplitComplex zsamples;
zsamples.realp = &X[0];
zsamples.imagp = &X[Nfloat/2];
t0 = uclock_sec();
for (iter = 0; iter < max_iter; ++iter) {
if (cplx) {
vDSP_fft_zip(setup, &zsamples, 1, log2N, kFFTDirection_Forward);
vDSP_fft_zip(setup, &zsamples, 1, log2N, kFFTDirection_Inverse);
} else {
vDSP_fft_zrip(setup, &zsamples, 1, log2N, kFFTDirection_Forward);
vDSP_fft_zrip(setup, &zsamples, 1, log2N, kFFTDirection_Inverse);
}
}
t1 = uclock_sec();
vDSP_destroy_fftsetup(setup);
flops = (max_iter*2) * ((cplx ? 5 : 2.5)*N*log((double)N)/M_LN2); // see http://www.fftw.org/speed/method.html
show_output("vDSP", N, cplx, flops, t0, t1, max_iter);
} else {
show_output("vDSP", N, cplx, -1, -1, -1, -1);
}
#endif
#ifdef HAVE_FFTW
{
fftwf_plan planf, planb;
fftw_complex *in = (fftw_complex*) fftwf_malloc(sizeof(fftw_complex) * N);
fftw_complex *out = (fftw_complex*) fftwf_malloc(sizeof(fftw_complex) * N);
memset(in, 0, sizeof(fftw_complex) * N);
int flags = (N < 40000 ? FFTW_MEASURE : FFTW_ESTIMATE); // measure takes a lot of time on largest ffts
//int flags = FFTW_ESTIMATE;
if (cplx) {
planf = fftwf_plan_dft_1d(N, (fftwf_complex*)in, (fftwf_complex*)out, FFTW_FORWARD, flags);
planb = fftwf_plan_dft_1d(N, (fftwf_complex*)in, (fftwf_complex*)out, FFTW_BACKWARD, flags);
} else {
planf = fftwf_plan_dft_r2c_1d(N, (float*)in, (fftwf_complex*)out, flags);
planb = fftwf_plan_dft_c2r_1d(N, (fftwf_complex*)in, (float*)out, flags);
}
t0 = uclock_sec();
for (iter = 0; iter < max_iter; ++iter) {
fftwf_execute(planf);
fftwf_execute(planb);
}
t1 = uclock_sec();
fftwf_destroy_plan(planf);
fftwf_destroy_plan(planb);
fftwf_free(in); fftwf_free(out);
flops = (max_iter*2) * ((cplx ? 5 : 2.5)*N*log((double)N)/M_LN2); // see http://www.fftw.org/speed/method.html
show_output((flags == FFTW_MEASURE ? "FFTW (meas.)" : " FFTW (estim)"), N, cplx, flops, t0, t1, max_iter);
}
#endif
// PFFFT benchmark
{
PFFFT_Setup *s = pffft_new_setup(N, cplx ? PFFFT_COMPLEX : PFFFT_REAL);
if (s) {
t0 = uclock_sec();
for (iter = 0; iter < max_iter; ++iter) {
pffft_transform(s, X, Z, Y, PFFFT_FORWARD);
pffft_transform(s, X, Z, Y, PFFFT_BACKWARD);
}
t1 = uclock_sec();
pffft_destroy_setup(s);
flops = (max_iter*2) * ((cplx ? 5 : 2.5)*N*log((double)N)/M_LN2); // see http://www.fftw.org/speed/method.html
show_output("PFFFT", N, cplx, flops, t0, t1, max_iter);
}
}
if (!array_output_format) {
printf("--\n");
}
pffft_aligned_free(X);
pffft_aligned_free(Y);
pffft_aligned_free(Z);
}
